Contradiction proof conception Prove: If A is true, then B is true Contradiction: If A is...

Contradiction proof conception

Prove: If A is true, then B is true

Contradiction: If A is true, then B is false.

so we suppose B is false and follow the step to prove. At the end we get if A is true then B is true so contradict our assumption

However,

Theorem: Let (xn) be a sequence in R. Let L∈R. If every subsequence of (xn) has a further subsequence that converges to L, then (xn) converges to L.

Proof: Assume, for contradiction, that (xn) doesn't converge to L

**my question is that at the end we will get no subsequence of (Xnk) converges to L (Xnk is a subsequence of Xn)****

why this is contradiction? This only shows the Contrapositive side of the theorem

Expert Solution

Colby Messinger answered 2 years ago

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